Theorem pm13.18

Description: Theorem *13.18 in WhiteheadRussell p. 178. (Contributed by Andrew Salmon, 3-Jun-2011) (Proof shortened by Wolf Lammen, 29-Oct-2024)

	Ref	Expression
Assertion	pm13.18	|- ( ( A = B /\ A =/= C ) -> B =/= C )

Proof

Step	Hyp	Ref	Expression
1		neeq1	|- ( A = B -> ( A =/= C <-> B =/= C ) )
2	1	biimpa	|- ( ( A = B /\ A =/= C ) -> B =/= C )